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Encyclopedia > Argument of periapsis

The argument of periapsis (ω) is the orbital element describing the angle between an orbiting body's ascending node (the point where the body crosses the plane of reference from South to North) and its periapsis (the point of closest approach to the central body), measured in the orbital plane and in the direction of motion. (For specific types of orbits, words such as "perihelion" (for Sun-centered orbits), "perigee" (for Earth-centered orbits), etc. may replace the word "periapsis". See apsis for more information.) The elements of an orbit are the parameters needed to specify that orbit uniquely, given a model of two ideal masses obeying the Newtonian laws of motion and the inverse-square law of gravitational attraction. ... This article is about angles in geometry. ... In physics, an orbit is the path that an object makes, around another object, whilst under the influence of a source of centripetal force, such as gravity. ... The ascending node is one of the orbital nodes, a point in the orbit of an object where it crosses the plane of the ecliptic from the south celestial hemisphere to the north celestial hemisphere in the direction of motion. ... In celestial mechanics, the plane of reference is the plane from which orbital elements are defined. ... A diagram of Keplerian orbital elements. ... The orbital plane of an object orbiting another is the geometrical plane in which the orbit is embedded. ... The Sun is the star of our solar system. ... Earth (IPA: , often referred to as the Earth, Terra, or Planet Earth) is the third planet in the solar system in terms of distance from the Sun, and the fifth largest. ... A diagram of Keplerian orbital elements. ...

An argument of periapsis of 0° means that the orbiting body will be at its closest approach to the central body at the same moment that it crosses the plane of reference from South to North. An argument of periapsis of 90° means that the orbiting body will reach periapsis at its northmost distance from the plane of reference.

Adding the argument of periapsis to the longitude of the ascending node gives the longitude of the periapsis. The Longitude of the ascending node () is one of the orbital elements used to specify the orbit of an object in space. ... In astrodynamics, the longitude of the periapsis (symbolized ) of an orbiting body is the longitude (measured from the point of the vernal equinox) of periapsis (closest approach to the central body). ...

Fig. 1: Diagram of orbital elements, including the argument of periapsis (ω).

Image File history File links Orbit. ... Image File history File links Orbit. ...

In astrodynamics the argument of periapsis $omega,$ can be calculated as follows: Astrodynamics is the study of the motion of rockets, missiles, and space vehicles, as determined from Sir Isaac Newtons laws of motion and his law of universal gravitation. ...

$omega = arccos { {mathbf{n} cdot mathbf{e}} over { mathbf{left |n right |} mathbf{left |e right |} }}$
(if $e_z < 0,$ then $omega = 2 pi - omega,$)

where:

• $mathbf{n}$ is the vector pointing towards the ascending node (i.e. the z-component of $mathbf{n}$ is zero),
• $mathbf{e }$ is the eccentricity vector (the vector pointing towards the periapsis).

In the case of equatorial orbits, though the argument is strictly undefined, it is often assumed that: In astrodynamics the eccentricity vector of a conic section orbit is the vector pointing towards the periapsis and with length equal to the orbits scalar eccentricity. ... Equatorial orbit is an orbit with inclination to the plane of reference (i. ...

$omega = arccos { {e_x} over { mathbf{left |e right |} }}$

where:

• $e_x,$ is x-component of the eccentricity vector $mathbf{e },$.

In the case of circular orbits it is often assumed that the periapsis is placed at the ascending node and therefore $omega=0,$.

Results from FactBites:

 Orbit - Printer-friendly - MSN Encarta (321 words) The size of the orbit is given by the periapsis distance (SP) and the elongation of the orbit is given by the eccentricity (e). The three orbital elements that describe an orbit's orientation are the inclination (i), the longitude of the ascending node (Ω), and the argument of the periapsis (ω). The argument of the periapsis is the angular displacement in the plane of the orbit between the ascending node and the line that passes through the centre of the orbit (C) and the periapsis (P).
 Argument of periapsis - Medbib.com, the modern encyclopedia (230 words) The argument of periapsis (ω) is the orbital element describing the angle between an orbiting body's ascending node (the point where the body crosses the plane of reference from South to North) and its periapsis (the point of closest approach to the central body), measured in the orbital plane and in the direction of motion. An argument of periapsis of 0° means that the orbiting body will be at its closest approach to the central body at the same moment that it crosses the plane of reference from South to North. An argument of periapsis of 90° means that the orbiting body will reach periapsis at its northmost distance from the plane of reference.
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